Units of Concentration
There are many different ways to express concentration of a solution.
Molarity is probably the most commonly used unit of concentration. It is the number of moles of solute per litre of solution (not necessarily the same as the volume of solvent). The SI unit of molarity is mol/dm3
Molality is defined as a concentration of moles per unit mass. With the weight of water being 1kg per litre, molality and molarity are interchangeable, however when diluting in for example ethanol, the weight of solution is different. SI units for molality is mol/kg
Parts per Million (ppm)
Parts per million works as percent by mass, but is a more convenient way of expressing concentration when there is only a small amount of solute present.
Therefore, ppm is defined as the mass of the component in solution divided by the total mass of the solution multiplied by 106 (one million):
A solution with a concentration of 1 ppm has 1 gram of substance for every million grams of solution.
Because the density of water is 1 gram per ml and if a tiny amount of solute is added, the density of a solution at such a low concentration remains approximately 1 gram per ml.
Therefore, in general, one ppm implies one milligram of solute per litre of solution.
A one percent solution is equivalent to 10,000 ppm. Therefore, something that has a concentration of 300 ppm could also be said to have a concentration of (300 ppm)/(10,000 ppm/percent) = 0.03% percent by mass.
Mass per Unit Volume (mg/ml or mg/cm3)
Some MSDS's (Material Safety Data Sheet) use milligrams per millilitre (mg/ml) or milligrams per cubic centimetre (mg/cm3). Note that 1 ml = 1 cm3 and that cm3 is sometimes denoted as a "cc”. Mass per unit volume is useful when expressing how soluble a material is in water or a particular solvent.
For example, "the solubility of substance X is 3 grams per litre". Percent by Mass (% w/w) also called weight percent or percent by weight, this is simply the mass of the solute divided by the total mass of the solution and multiplied by 100%.
Whilst the unit is archaic in modern chemistry, it is still used in medicine and found in older papers. It is defined as the molar concentration divided by an equivalent factor. It can be expressed as eq/l (equivalent per liter) or meq/l (millieqivalent per litre of 0.001N which can be found in medical reports). It is can either be based on its electron displacement, or on acid/base displacement.
For example a solution of HNO3 with a concentration of 1M would have a normality concentration of 1N, as one mole of hydrogen ions is displaced per mole of nitric acid.
A solution of barium hydroxide (Ba(OH)2) of concentration 0.5M would have a normality of 1N, as one mole of barium hydroxide displaces two hydroxide ions per mole of barium hydroxide.
A solution of Aluminium Chloride (AlCl3) with a concentration of 0.25M would have a normality of 0.75N, due to Aluminium displacing 3 electrons; therefor the normality is 3 times greater than the molarity.
Geyer, Robert & Bowie, E.‘The Direct Microdetermination of Tissue Calcium
by Flame Photometry’,Anal Biochem, 2, (1961), p. 360-369.